Why Recursion Fails: The Overlapping Subproblem Trap

Recursion looks clean, but overlapping subproblems can quickly cause exponential time complexity. In this video, we break down why naive recursive solutions repeatedly recompute the same values using the Fibonacci sequence as a concrete example. You'll learn: • What overlapping subproblems are and how to spot them • Why recursive tree branching leads to duplicate calculations • How to optimize recursion using array memoization / tabulation • How to achieve an optimal O(1) space complexity solution in Swift Mastering this core concept is essential for tackling dynamic programming and algorithm interview questions. Timestamps: 0:00 - Introduction to Overlapping Subproblems 0:35 - Visualizing Redundant Calls with Fibonacci 2:15 - Solution 1: Array-Based Tabulation (O(N) Space) 3:35 - Solution 2: Constant Space Optimization (O(1) Space) 4:05 - Performance & Execution Time Comparison